8.3.5. Two-Fluid Model¶
This section contains keywords relating to the Two-Fluid Model.
8.3.5.1. KT_TYPE¶
Data Type: CHARACTER
Applies to Solids Model(s): TFM
Solids phase stress model [Algebraic].
Name |
Default? |
Description |
|---|---|---|
|
◉ |
Granular energy algebraic formulation. |
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Cao and Ahmadi (1995). Int. J. Multiphase Flow 21(6), 1203. |
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Garzo and Dufty (1999). Phys. Rev. E 59(5), 5895. |
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Garzo, Hrenya and Dufty (2007). Phys. Rev. E 76(3), 31304 |
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Garzo, Tenneti, Subramaniam, Hrenya (2012). J.Fluid Mech. 712, 129. |
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Iddir & Arastoopour (2005). AIChE J. 51(6), 1620 |
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Lun et al (1984). J. Fluid Mech., 140, 223. |
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Simonin (1996). VKI Lecture Series, 1996-2 |
8.3.5.2. FRICTION_MODEL¶
Data Type: CHARACTER
Applies to Solids Model(s): TFM
Solids stress friction model selection.
Name |
Default? |
Description |
|---|---|---|
|
Only solids pressure |
|
|
◉ |
Schaeffer friction model. 1987, Journal of Differential Equations 66, 19–50. |
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Srivastava and Sundaresan friction model. 2003, Powder Technology 129(1-3):72-85 |
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Guo-Boyce friction model, 2021. Proceedings of the National Academy of Sciences, 118 (35). |
8.3.5.3. BLENDING_FUNCTION¶
Data Type: CHARACTER
Applies to Solids Model(s): TFM
Blend the Schaeffer stresses with the stresses resulting from algebraic kinetic theory around the value of EP_STAR. [NONE]
Name |
Default? |
Description |
|---|---|---|
|
◉ |
No blending |
|
Hyperbolic tangent function |
|
|
Scaled sigmodial function |
8.3.5.4. YU_STANDISH¶
Data Type: LOGICAL
Applies to Solids Model(s): TFM
Use Yu-Standish correlation to compute maximum packing for polydisperse systems.
A.B. Yu and N. Standish. Powder Tech, 52 (1987) 233-241
Name |
Default? |
Description |
|---|---|---|
|
Use the Yu-Standish correlation. |
|
|
◉ |
Do not use the Yu-Standish correlation. |
8.3.5.5. FEDORS_LANDEL¶
Data Type: LOGICAL
Applies to Solids Model(s): TFM
Use Fedors-Landel correlation to compute maximum packing for binary (only) mixtures of powders.
R.F. Fedors and R.F. Landel. Powder Tech, 23 (1979) 225-231
Name |
Default? |
Description |
|---|---|---|
|
Use the Fedors-Landel correlation. |
|
|
◉ |
Do not use the Fedors-Landel correlation. |
8.3.5.6. RDF_TYPE¶
Data Type: CHARACTER
Applies to Solids Model(s): TFM
Radial distribution function (RDF) at contact.
Name |
Default? |
Description |
|---|---|---|
|
Carnahan, N.F. and Starling K.E., (1969). The Journal of Chemical Physics, Vol. 51(2):635-636. Only applies to monodisperse cases. |
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Ma, D. and Ahmadi, G., (1986). The Journal of Chemical Physics, 84(6):3449. Only applies to monodisperse cases. |
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Lebowitz, J.L. (1964) The Physical Review, A133, 895-899. Only applies to polydisperse cases. |
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Iddir, H. Y., Modeling of the multiphase mixture of particles using the kinetic theory approach. Doctoral Dissertation, Illinois Institute of Technology, Chicago, Illinois, 2004, (chapter 2, equations 2-49 through 2-52.) Only applies to polydisperse cases. |
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Mansoori, GA, Carnahan N.F., Starling, K.E. Leland, T.W. (1971). The Journal of Chemical Physics, Vol. 54:1523-1525. Only applies to polydisperse cases. |
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van Wachem, B.G.M., Schouten, J.C., van den Bleek, C.M., Krishna, R. and Sinclair, J. L. (2001) AIChE Journal 47:1035–1051. Only applies to polydisperse cases. |
8.3.5.7. ADDED_MASS¶
Data Type: LOGICAL
Applies to Solids Model(s): TFM
Flag to include the added (or virtual) mass force. This force acts to increase the inertia of the dispersed phase, which tends to stabilize simulations of bubbly gas-liquid flows.
8.3.5.8. M_AM¶
Data Type: INTEGER
Applies to Solids Model(s): TFM
The disperse phase number to which the added mass is applied.
8.3.5.9. C_E¶
Data Type: DOUBLE PRECISION
Applies to Solids Model(s): TFM
Coefficient of restitution for particle-particle collisions.
8.3.5.10. R_P(PHASE, PHASE)¶
Data Type: DOUBLE PRECISION
\(1 \le Phase \le 2\)
\(1 \le Phase \le 2\)
Coefficient of restitution for particle-particle collisions specific to GHD theory implementation.
8.3.5.11. E_W¶
Data Type: DOUBLE PRECISION
Coefficient of restitution for particle-wall collisions when using Johnson and Jackson partial slip BC (BC_JJ_PS).
8.3.5.12. PHIP¶
Data Type: DOUBLE PRECISION
Applies to Solids Model(s): TFM
Specularity coefficient associated with particle-wall collisions when using Johnson and Jackson partial slip BC (BC_JJ_PS). If Jenkins small frictional BC are invoked (JENKINS) then PHIP is not used.
8.3.5.13. PHIP0¶
Data Type: DOUBLE PRECISION
Applies to Solids Model(s): TFM
Specify the value of specularity coefficient when the normalized slip velocity goes to zero when BC_JJ_M is .TRUE.. This variable is calculated internally in MFiX. Do not modify unless an accurate number is known.
8.3.5.14. C_F¶
Data Type: DOUBLE PRECISION
Applies to Solids Model(s): TFM
Coefficient of friction between the particles of two solids phases.
8.3.5.15. PHI¶
Data Type: DOUBLE PRECISION
Applies to Solids Model(s): TFM
Angle of internal friction (in degrees). Set this value to zero to turn off plastic regime stress calculations.
8.3.5.16. PHI_W¶
Data Type: DOUBLE PRECISION
Applies to Solids Model(s): TFM
Angle of internal friction (in degrees) at walls. Set this value to non-zero (PHI_W = 11.31 means TAN_PHI_W = MU = 0.2) when using Johnson and Jackson partial slip BC (BC_JJ_PS) with Friction model or Jenkins small frictional boundary condition.
8.3.5.17. EPS_F_MIN¶
Data Type: DOUBLE PRECISION
Applies to Solids Model(s): TFM
Minimum solids fraction above which friction sets in. [0.5]
8.3.5.18. EP_S_MAX(PHASE)¶
Data Type: DOUBLE PRECISION
\(1 \le Phase \le 10\)
Applies to Solids Model(s): TFM
Maximum solids volume fraction at packing for polydisperse systems (more than one solids phase used). The value of EP_STAR may change during the computation if solids phases with different particle diameters are specified and Yu_Standish or Fedors_Landel correlations are used.
8.3.5.19. SEGREGATION_SLOPE_COEFFICIENT¶
Data Type: DOUBLE PRECISION
Applies to Solids Model(s): TFM
Used in calculating the initial slope of segregation: see Gera et al. (2004) - recommended value 0.3. Increasing this coefficient results in decrease in segregation of particles in binary mixtures.
8.3.5.20. V_EX¶
Data Type: DOUBLE PRECISION
Applies to Solids Model(s): TFM
Excluded volume in Boyle-Massoudi stress.
Name |
Default? |
Description |
|---|---|---|
|
Boyle-Massoudi stress is turned off. |
8.3.5.21. MU_S0(PHASE)¶
Data Type: DOUBLE PRECISION
\(1 \le Phase \le 10\)
Applies to Solids Model(s): TFM
Specified constant viscosity. If any value is specified then:
- kinetic theory calculations (granular_energy) are off, which
means zero granular pressure contribution (P_S = 0)
- frictional/plastic calculations are off, which means zero
frictional viscosity contributions, however, a plastic pressure term is still invoked (P_STAR)
LAMBDA_S = -2/3 MU_S0
8.3.5.22. DIF_S0(PHASE)¶
Data Type: DOUBLE PRECISION
\(1 \le Phase \le 10\)
Applies to Solids Model(s): TFM
Specified constant solids diffusivity [m^2/s in SI].
8.3.5.23. EP_STAR¶
Data Type: DOUBLE PRECISION
Applies to Solids Model(s): TFM
Packed bed void fraction. Used to calculate plastic stresses (for contribution to viscosity) and when to implement plastic pressure, P_STAR. Specifically, if EP_G < EP_STAR, then plastic pressure is employed in the momentum equations.
8.3.5.24. CLOSE_PACKED(PHASE)¶
Data Type: LOGICAL
\(1 \le Phase \le 10\)
Applies to Solids Model(s): TFM
Flag to enable/disable a phase from forming a packed bed. Effectively removes plastic pressure term from the solids phase momentum equation.
Name |
Default? |
Description |
|---|---|---|
|
◉ |
The phase forms a packed bed with void fraction EP_STAR. |
|
The phase can exceed close pack conditions so that it maybe behave like a liquid. |
8.3.5.25. JENKINS¶
Data Type: LOGICAL
This flag affects how the momentum and granular energy boundary conditions are implemented when using BC_JJ_PS BC.
Name |
Default? |
Description |
|---|---|---|
|
◉ |
Use standard boundary conditions. |
|
Use Jenkins small frictional boundary condition. |